We humans are pretty good at understanding linear change. It's all around us:
--eat more, gain some weight; eat less, lose some weight
--press on the gas pedal, speed up; press on the brake, slow down
--turn up the heat, feel warmer; turn down the heat, feel cooler
--someone can't hear you, talk louder; someone moves closer, talk more softly
--and thousands of other daily experiences in which a small change produces a small result and a larger change produces a larger result.
However, some events don't behave linearly. There are situations where a small change can produce a big effect. We're living through at least two of them right now--the Covid-19 pandemic and climate change. Unfortunately, we're failing miserably in understanding and dealing with both of them.
Let's do a little math--please bear with me:
Step number//Linear growth (n x 2)// Exponential growth (2 to the n)
1......................................2 ...................................... 2
2......................................4........................................4
3......................................6........................................8
4......................................8......................................16
5....................................10......................................32
6....................................12......................................64
7....................................14....................................128
8....................................16....................................256
9....................................18....................................512
10..................................20..................................1024
11..................................22................................. 2048
The steps might represent weeks. The first column might represent a situation where the virus is fairly well controlled (e.g. through some combination of social distancing, mask wearing, testing, tracing and isolating people likely to shed the virus). On average one infected person infects approximately one other person, with the result that the number of cases grows linearly. The third column represents exponential growth--where the virus truly is "going viral." All that takes is for one infected person to pass the virus on to more than one new victim.
Notice the enormous and rapidly expanding difference as the weeks tick by. At week three, exponential growth has infected just two more people than in the linear growth model, but at ten weeks the difference is more than 1,000, and one week later, more than 2,000.
So, our first takeaway is that when we're dealing with any situation involving exponential growth, at first it's hard to distinguish from the linear progressions that we're used to, but sooner or later it takes off explosively.
Now let's examine that phrase "sooner or later."
Week// Doubling stopped sooner// Doubling stopped later
1.................................2...................................2
2.................................4...................................4
3.................................8...................................8
4...............................16.................................16
5...............................18.................................32
6...............................20.................................64
7...............................22...............................128
8...............................24...............................256
9...............................26...............................258
10.............................28...............................260
11.............................30...............................262
Total Cases:..........198.............................1290
What a difference a delay makes. This might represent two states, one
of which sees the exponential handwriting on the wall after just four
weeks, institutes effective controls and ends up with 198 cases, while
the other delays control measures one month more and ends up with with
6.5 times as many cases. (Or these numbers could equally well represent
deaths, in which case that one month delay would have caused over a
thousand needless deaths.
Obviously the numbers above are meant to be an illustration; they don't
match exactly with the real world. However, you can see this in actual cases and deaths if you compare the impact of a one-week delay in responding to
the pandemic in New York vs. California. Here's a zerospinzone.blogspot post from March 30:
You can
see what difference even a few days lag in imposing strict stay-at-home
orders makes. California--population 39.5 million, first state to
impose strict controls: current # of cases 6358, deaths 132. New
York--population 19.5 million, delayed a week before imposing controls:
current # of cases 60,679, deaths 1063. The number of cases per
population in NY is 19 times greater than in California, and the number
of deaths per population 17 times greater. What a tragic difference a
week's delay makes.
Clamping down just one
week earlier in California has almost certainly saved tens of thousands of
lives by now.
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